This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

Hydroelastic vibration of rectangular plates

A note on vibration of a cantilever plate immersed in water

Free vibration analysis of cantilever plate partially submerged into a fluid

Numerical and experimental analysis of the dynamic response of large submerged trash-racks

The paper presents the results of investigations conducted to evaluate the added mass to represent fluid-structure interaction effects in vibration/dynamic analysis of floating bodies such as ship hulls While the structural plating is idealized by 9-noded plate/shell finite elements, the fluid domain is modelled by 20-noded/21-noded 3-D finite elements in the investigations conducted A new 8-noded element has been developed to model the interface between the structure and the fluid An efficient computational methodology has been used for computation of added mass The finite element models are validated by comparing the results with those given by analytical solution for a submerged sphere The efficacy of the finite element model is demonstrated through convergence of the results obtained for a floating barge problem A better convergence rate and distribution of added mass in three orthogonal directions have been obtained

A new 3‐D finite element model to evaluate added mass for analysis of fluid‐structure interaction problems

The equations for the free undamped vibration of a structure in an ideal incompressible fluid medium and their finite element formulation are briefly reviewed. The relevant matrices (stiffness and loading) for two prismatic fluid elements are given explicitly and some numerical results are presented.

P C Chowdhury

Papers

Fluid finite elements for added mass calculations